化简 x/(x+4)-(2x)/(x+2)

解答

化简

\frac{x}{x + 4} - \frac{2 x}{x + 2}

\frac{- x ^{2} - 6 x}{( x + 4 ) ( x + 2 )}

求解步骤

\frac{x}{x + 4} - \frac{2 x}{x + 2}

x + 4, x + 2

的最小公倍数:

(x + 4) (x + 2)

根据最小公倍数调整分式

= \frac{x ( x + 2 )}{( x + 4 ) ( x + 2 )} - \frac{2 x ( x + 4 )}{( x + 4 ) ( x + 2 )}

使用分式法则:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{x ( x + 2 ) - 2 x ( x + 4 )}{( x + 4 ) ( x + 2 )}

化简

x (x + 2) - 2 x (x + 4) : - x^{2} - 6 x

= \frac{- x ^{2} - 6 x}{( x + 4 ) ( x + 2 )}

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